Problem: Solve for $x$ and $y$ using elimination. ${6x-2y = 28}$ ${5x-2y = 23}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $-1$ ${6x-2y = 28}$ $-5x+2y = -23$ Add the top and bottom equations together. ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {6x-2y = 28}\thinspace$ to find $y$ ${6}{(5)}{ - 2y = 28}$ $30-2y = 28$ $30{-30} - 2y = 28{-30}$ $-2y = -2$ $\dfrac{-2y}{{-2}} = \dfrac{-2}{{-2}}$ ${y = 1}$ You can also plug ${x = 5}$ into $\thinspace {5x-2y = 23}\thinspace$ and get the same answer for $y$ : ${5}{(5)}{ - 2y = 23}$ ${y = 1}$